Question: ${\sqrt[3]{1000} = \text{?}}$
Answer: $\sqrt[3]{1000}$ is the number that, when multiplied by itself three times, equals $1000$ If you can't think of that number, you can break down $1000$ into its prime factorization and look for equal groups of numbers. So the prime factorization of $1000$ is $2\times 2\times 2\times 5\times 5\times 5$ We're looking for $\sqrt[3]{1000}$ , so we want to split the prime factors into three identical groups. Notice that we can rearrange the factors like so: $1000 = 2\times 2\times 2\times 5\times 5\times 5 = \left(2\times 5\right)\times\left(2\times 5\right)\times\left(2\times 5\right)$ So $\left(2\times 5\right)^3 = 10^3 = 1000$ So $\sqrt[3]{1000}$ is $10$.